No one will insure you because what your doing is totally illegal. While India looks like disorganized anarchy they do in fact have a strict legal system!!
Often many travellers don't have anything of the sort, not even riding experience... In fact, the first Enfield I bought I had no license of any sort, and no papers for the bike, certainly no insurance! Luckily, apart from falling off and looking stupid a few times, I never got caught or had an accident.
The law says that to drive a vehicle in India you must be legally allowed to do so in your own country. In actual fact, if the cops stop you can you can produce a car license and maybe an international counterpart, they'll probably be satisfied with that.
Yet if you were to have an accident or get into trouble with the police, and it went to court, etc, then you could get into a lot of trouble because you were driving illegally and this could make even a minor road accident a criminal investigation.
You'll also need to produce the papers of the bike and maybe insurance for the vehicle. This is not travel insurance nor will it be of any use to you in an accident. I think it is third-party; all vehicles need to have this to be legally allowed on the road. I'm unsure of the specifics, however.
Even if you find a 125cc, I suspect you might have been mistaken about being insured on it. Often, travel insurance companies may insure you on scooters, and to ride pillion, but 'touring' is a different category (i.e. prolonged use of motorcycle for purposes of travel, tourism, adventure tourism etc). So be VERY careful and ask your insurer before. I asked several would they insure me in S.America on a 125 with my CBT and/or car license and none of them would.
Hope that helps,